We recognize that we have an expression in the form (x + y)(x − y) and recall from earlier algebra that this is equal to the difference of 2 squares.
(x + y)(x − y) = x2 − y2
We use this to find our answer as follows:
`(5 + sqrt(a))(5 - sqrt(a))` ` =5^2 - (sqrt(a))^2` ` = 25 -a `
Notice that our final answer does not have a square root sign. We now havea rational answer (since there are no radicals in it).
This idea is important in the next section, where we use it to rationalize the denominator of a fraction.